Shooting with two hands does make you more accurate, depending on the style.
What Bicycle Repaiman was referring to earlier in CQB is called "weapon's retention," but that is not quite the same thing. You see, soldiers are taught now to hold their pistols clost to their chest for retaining them (i.e. keeping them from being grabbed by an enemy or hysterical bystander) in close quarters, but when they actually need to take a shot, they are taught to extend their arms outward to full length, so really you end up with your gun out there just as much as with one hand, as far as retention is concerned.
Now, as for actualy accuracy, the two handed "instinctive shooting" style has suposedly been found to reduce trembling due to stress and the fact that in combat, you are probably breathing hard, etc. Also, it places the weapon right in front of your eyes, to you have a straight and simple aim point, and many times this stance is taught with the idea that you aim *over* the sights of the weapon, focusing on the target more than on the sight picture.
Finally, it is better because you don't turn you body to one side, but stand with your legs shoulder width apart, knees flexed, and shoulders slightly "hunched," all of this is also suppossed to decrease the effects of trembling and improve balance. This type of shooting has only been developed since the late 70s and early 80s, and even then only SWAT/HRT style operatives used it. Only in the last few years has the standard GI been taught to shoot like this.
As far as WWII is concerned, I agree with the people that say that a soldier will not really shoot far outside how he was taught: training makes people revert back on what they learned through repetition, in combat this repetition is all that a solider has. Also, I disagree with the people that think soldier's would have adopted two-handed, Weaver style stances instinctively because it is "better." Why do you ask? Well consider a modern conflict:
In Iraq, I have seen tons of pictures lately of guys running around holding their M16s with their supporting hand on the *magazine well*, yes you heard me, the friggin magazine well.
Now why is this bad? For one, a full length rifle like the A2 or A3 is *always* going to shoot better by holding it properly with the supporting hand on the forearm--they are are not SMGs or MPs where you are supposed to hold them around the magazine. This throws off you center of balance on the weapon, causing your barrel to "droop" more, and it is a lot easier for someone to grab the end of the rifle and pull the weapon away from you (once again the idea of weapon's retention).
However, the biggest thing that hits me when I see those pictues, is the idea that those guys are all two secons away from having their magazines drop out. If anyone has held an M16 (I own a CAR 15 myself), then you know that the mag release catch is right there on the side of the well. Basically, if you wrap your hand around the well likes its a grip, you are just asking for your fingers or palm (depending on if you are left or right handed) to hit hte mag release---this is ieven more likely if you have a tight grip under anxiety.
In summation, that is about the WORST way you can carry an M16 in a combat environment, but you see soldiers doing it all over TV and in pictures. So, do men really do what is "better" or more accurate? No. But, do they do what they were trained by some yokel DI or what "looks sexy," yes they do, apparently.